{
 "schema_version": "0.4",
 "name": "[[85,8,9]]",
 "code_type": "stabilizer",
 "n": 85,
 "k": 8,
 "checks": {
  "S": [
   {
    "X": [
     0,
     4,
     19
    ],
    "Z": [
     0,
     1,
     26
    ]
   },
   {
    "X": [
     3,
     16,
     18
    ],
    "Z": [
     1,
     2,
     27
    ]
   },
   {
    "X": [
     2,
     15,
     17
    ],
    "Z": [
     2,
     3,
     28
    ]
   },
   {
    "X": [
     1,
     14,
     33
    ],
    "Z": [
     3,
     4,
     29
    ]
   },
   {
    "X": [
     0,
     13,
     32
    ],
    "Z": [
     4,
     5,
     30
    ]
   },
   {
    "X": [
     12,
     16,
     31
    ],
    "Z": [
     5,
     6,
     31
    ]
   },
   {
    "X": [
     11,
     15,
     30
    ],
    "Z": [
     6,
     7,
     32
    ]
   },
   {
    "X": [
     10,
     14,
     29
    ],
    "Z": [
     7,
     8,
     33
    ]
   },
   {
    "X": [
     9,
     13,
     28
    ],
    "Z": [
     8,
     9,
     17
    ]
   },
   {
    "X": [
     8,
     12,
     27
    ],
    "Z": [
     9,
     10,
     18
    ]
   },
   {
    "X": [
     7,
     11,
     26
    ],
    "Z": [
     10,
     11,
     19
    ]
   },
   {
    "X": [
     6,
     10,
     25
    ],
    "Z": [
     11,
     12,
     20
    ]
   },
   {
    "X": [
     5,
     9,
     24
    ],
    "Z": [
     12,
     13,
     21
    ]
   },
   {
    "X": [
     4,
     8,
     23
    ],
    "Z": [
     13,
     14,
     22
    ]
   },
   {
    "X": [
     3,
     7,
     22
    ],
    "Z": [
     14,
     15,
     23
    ]
   },
   {
    "X": [
     2,
     6,
     21
    ],
    "Z": [
     15,
     16,
     24
    ]
   },
   {
    "X": [
     1,
     5,
     20
    ],
    "Z": [
     0,
     16,
     25
    ]
   },
   {
    "X": [
     2,
     68,
     72
    ],
    "Z": [
     17,
     18,
     43
    ]
   },
   {
    "X": [
     1,
     71,
     84
    ],
    "Z": [
     18,
     19,
     44
    ]
   },
   {
    "X": [
     0,
     70,
     83
    ],
    "Z": [
     19,
     20,
     45
    ]
   },
   {
    "X": [
     16,
     69,
     82
    ],
    "Z": [
     20,
     21,
     46
    ]
   },
   {
    "X": [
     15,
     68,
     81
    ],
    "Z": [
     21,
     22,
     47
    ]
   },
   {
    "X": [
     14,
     80,
     84
    ],
    "Z": [
     22,
     23,
     48
    ]
   },
   {
    "X": [
     13,
     79,
     83
    ],
    "Z": [
     23,
     24,
     49
    ]
   },
   {
    "X": [
     12,
     78,
     82
    ],
    "Z": [
     24,
     25,
     50
    ]
   },
   {
    "X": [
     11,
     77,
     81
    ],
    "Z": [
     25,
     26,
     34
    ]
   },
   {
    "X": [
     10,
     76,
     80
    ],
    "Z": [
     26,
     27,
     35
    ]
   },
   {
    "X": [
     9,
     75,
     79
    ],
    "Z": [
     27,
     28,
     36
    ]
   },
   {
    "X": [
     8,
     74,
     78
    ],
    "Z": [
     28,
     29,
     37
    ]
   },
   {
    "X": [
     7,
     73,
     77
    ],
    "Z": [
     29,
     30,
     38
    ]
   },
   {
    "X": [
     6,
     72,
     76
    ],
    "Z": [
     30,
     31,
     39
    ]
   },
   {
    "X": [
     5,
     71,
     75
    ],
    "Z": [
     31,
     32,
     40
    ]
   },
   {
    "X": [
     4,
     70,
     74
    ],
    "Z": [
     32,
     33,
     41
    ]
   },
   {
    "X": [
     3,
     69,
     73
    ],
    "Z": [
     17,
     33,
     42
    ]
   },
   {
    "X": [
     51,
     55,
     70
    ],
    "Z": [
     34,
     35,
     60
    ]
   },
   {
    "X": [
     54,
     67,
     69
    ],
    "Z": [
     35,
     36,
     61
    ]
   },
   {
    "X": [
     53,
     66,
     68
    ],
    "Z": [
     36,
     37,
     62
    ]
   },
   {
    "X": [
     52,
     65,
     84
    ],
    "Z": [
     37,
     38,
     63
    ]
   },
   {
    "X": [
     51,
     64,
     83
    ],
    "Z": [
     38,
     39,
     64
    ]
   },
   {
    "X": [
     63,
     67,
     82
    ],
    "Z": [
     39,
     40,
     65
    ]
   },
   {
    "X": [
     62,
     66,
     81
    ],
    "Z": [
     40,
     41,
     66
    ]
   },
   {
    "X": [
     61,
     65,
     80
    ],
    "Z": [
     41,
     42,
     67
    ]
   },
   {
    "X": [
     60,
     64,
     79
    ],
    "Z": [
     42,
     43,
     51
    ]
   },
   {
    "X": [
     59,
     63,
     78
    ],
    "Z": [
     43,
     44,
     52
    ]
   },
   {
    "X": [
     58,
     62,
     77
    ],
    "Z": [
     44,
     45,
     53
    ]
   },
   {
    "X": [
     57,
     61,
     76
    ],
    "Z": [
     45,
     46,
     54
    ]
   },
   {
    "X": [
     56,
     60,
     75
    ],
    "Z": [
     46,
     47,
     55
    ]
   },
   {
    "X": [
     55,
     59,
     74
    ],
    "Z": [
     47,
     48,
     56
    ]
   },
   {
    "X": [
     54,
     58,
     73
    ],
    "Z": [
     48,
     49,
     57
    ]
   },
   {
    "X": [
     53,
     57,
     72
    ],
    "Z": [
     49,
     50,
     58
    ]
   },
   {
    "X": [
     52,
     56,
     71
    ],
    "Z": [
     34,
     50,
     59
    ]
   },
   {
    "X": [
     34,
     38,
     53
    ],
    "Z": [
     51,
     52,
     77
    ]
   },
   {
    "X": [
     37,
     50,
     52
    ],
    "Z": [
     52,
     53,
     78
    ]
   },
   {
    "X": [
     36,
     49,
     51
    ],
    "Z": [
     53,
     54,
     79
    ]
   },
   {
    "X": [
     35,
     48,
     67
    ],
    "Z": [
     54,
     55,
     80
    ]
   },
   {
    "X": [
     34,
     47,
     66
    ],
    "Z": [
     55,
     56,
     81
    ]
   },
   {
    "X": [
     46,
     50,
     65
    ],
    "Z": [
     56,
     57,
     82
    ]
   },
   {
    "X": [
     45,
     49,
     64
    ],
    "Z": [
     57,
     58,
     83
    ]
   },
   {
    "X": [
     44,
     48,
     63
    ],
    "Z": [
     58,
     59,
     84
    ]
   },
   {
    "X": [
     43,
     47,
     62
    ],
    "Z": [
     59,
     60,
     68
    ]
   },
   {
    "X": [
     42,
     46,
     61
    ],
    "Z": [
     60,
     61,
     69
    ]
   },
   {
    "X": [
     41,
     45,
     60
    ],
    "Z": [
     61,
     62,
     70
    ]
   },
   {
    "X": [
     40,
     44,
     59
    ],
    "Z": [
     62,
     63,
     71
    ]
   },
   {
    "X": [
     39,
     43,
     58
    ],
    "Z": [
     63,
     64,
     72
    ]
   },
   {
    "X": [
     38,
     42,
     57
    ],
    "Z": [
     64,
     65,
     73
    ]
   },
   {
    "X": [
     37,
     41,
     56
    ],
    "Z": [
     65,
     66,
     74
    ]
   },
   {
    "X": [
     36,
     40,
     55
    ],
    "Z": [
     66,
     67,
     75
    ]
   },
   {
    "X": [
     35,
     39,
     54
    ],
    "Z": [
     51,
     67,
     76
    ]
   },
   {
    "X": [
     17,
     21,
     36
    ],
    "Z": [
     9,
     68,
     69
    ]
   },
   {
    "X": [
     20,
     33,
     35
    ],
    "Z": [
     10,
     69,
     70
    ]
   },
   {
    "X": [
     19,
     32,
     34
    ],
    "Z": [
     11,
     70,
     71
    ]
   },
   {
    "X": [
     18,
     31,
     50
    ],
    "Z": [
     12,
     71,
     72
    ]
   },
   {
    "X": [
     17,
     30,
     49
    ],
    "Z": [
     13,
     72,
     73
    ]
   },
   {
    "X": [
     29,
     33,
     48
    ],
    "Z": [
     14,
     73,
     74
    ]
   },
   {
    "X": [
     28,
     32,
     47
    ],
    "Z": [
     15,
     74,
     75
    ]
   },
   {
    "X": [
     27,
     31,
     46
    ],
    "Z": [
     16,
     75,
     76
    ]
   },
   {
    "X": [
     26,
     30,
     45
    ],
    "Z": [
     0,
     76,
     77
    ]
   },
   {
    "X": [
     25,
     29,
     44
    ],
    "Z": [
     1,
     77,
     78
    ]
   },
   {
    "X": [
     24,
     28,
     43
    ],
    "Z": [
     2,
     78,
     79
    ]
   },
   {
    "X": [
     23,
     27,
     42
    ],
    "Z": [
     3,
     79,
     80
    ]
   },
   {
    "X": [
     22,
     26,
     41
    ],
    "Z": [
     4,
     80,
     81
    ]
   },
   {
    "X": [
     21,
     25,
     40
    ],
    "Z": [
     5,
     81,
     82
    ]
   },
   {
    "X": [
     20,
     24,
     39
    ],
    "Z": [
     6,
     82,
     83
    ]
   },
   {
    "X": [
     19,
     23,
     38
    ],
    "Z": [
     7,
     83,
     84
    ]
   },
   {
    "X": [
     18,
     22,
     37
    ],
    "Z": [
     8,
     68,
     84
    ]
   }
  ]
 },
 "distance": {
  "d": 9,
  "P": {
   "value": 9,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     18,
     43,
     44,
     57,
     64
    ],
    "Z": [
     27,
     42,
     46,
     58,
     64
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mrvee-qC-bee",
   "Andrey Boris Khesin",
   "Jonathan Z. Lu"
  ],
  "construction": "Published abelian mirror code, arXiv:2603.05496v1 Section 5. G has cyclic factors [5, 17], A=[(0, 0), (0, 1), (1, 9)], B=[(0, 0), (0, 4), (1, 2)]. Lexicographic qubits g; each generator has Z on A+g and X on B-g.",
  "origin": "submission",
  "date": "2026-10-01",
  "model": "GPT-6 Astra",
  "notes": "Literature reproduction. Numerical distance is a witnessed upper bound; no new-construction claim.",
  "novelty": "known_parameters",
  "references": [
   "https://arxiv.org/abs/2603.05496"
  ]
 },
 "family": "other"
}
